Siberian Mathematical Journal

, Volume 26, Issue 2, pp 198–216 | Cite as

Multipliers in spaces with “fractional” norms, and inner functions

  • I. É. Verbitskii


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Literature Cited

  1. 1.
    V. G. Maz'ya, “Strong capacity estimates for ‘fractional’ norms,” J. Sov. Math.,23, No. 1 (1983).Google Scholar
  2. 2.
    V. G. Maz'ya, “Multipliers in Sobolev spaces,” in: Applications of the Methods of the Theory of Functions and Functional Analysis to Problems of Mathematical Physics [in Russian], Novosibirsk (1978), pp. 181–189.Google Scholar
  3. 3.
    V. G. Maz'ya and T. O. Shaposhnikova, “Multipliers in function spaces with fractional derivatives,” Dokl. Akad. Nauk SSSR,244, No. 5, 1065–1067 (1979).Google Scholar
  4. 4.
    V. G. Maz'ya and T. O. Shaposhnikova, “Multipliers in spaces of differentiable functions,” in: Theory of Cubature Formulas and the Application of Functional Analysis to Problems of Mathematical Physics, Tr. Sem. S. L. Sobolev,1979, No. 1, Inst. Mat. Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1979), pp. 39–90.Google Scholar
  5. 5.
    D. A. Stegenga, “Multipliers of Dirichlet, spaces,” Illinois J. Math.,24, No. 1, 113–140 (1980).Google Scholar
  6. 6.
    K. Hoffman, Banach Spaces of Analytic Functions [Russian translation], IL, Moscow (1962).Google Scholar
  7. 7.
    I. I. Hirschman Jr., “On multiplier transformations. II,” Duke Math. J.,28, No. 1, 45–46 (1961).Google Scholar
  8. 8.
    I. I. Hirschman Jr., “On multiplier transformations. III,” Proc. Am. Math. Soc.,13, No. 5, 851–857 (1962).Google Scholar
  9. 9.
    G. D. Taylor, “Multipliers on Dα,” Trans. Am. Math. Soc.,123, No. 2, 229–240 (1966).Google Scholar
  10. 10.
    R. S. Strichartz “Multipliers on fractional Sobolev spaces,” J. Math. Mech.,16, No. 9, 1031–1060 (1967).Google Scholar
  11. 11.
    D. R. Adams, “On the existence of capacity strong type estimates in Rn,” Arkiv. Mat.,14, No. 1, 125–140 (1976).Google Scholar
  12. 12.
    D. J. Newman and H. S. Shapiro, “The Taylor coefficients of inner functions,” Michigan Math. J.,9, No. 2, 249–255 (1962).Google Scholar
  13. 13.
    L. Carleson, On a class of Meromorphic Functions and Its Associated Exceptional Sets, Thesis, University of Upsala (1950).Google Scholar
  14. 14.
    V. G. Maz'ya, “Summability with respect to an arbitrary measure of functions from Sobolev-Slobodetskii spaces” Investigations on Linear Operators and the Theory of Functions. IX, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Steklov (LOMI),92, 192–202 (1979).Google Scholar
  15. 15.
    P. Ahern and D. N. Clark, “On inner functions with BP-derivatives,” Michigan Math. J.,23, No. 1, 107–118 (1976).Google Scholar
  16. 16.
    P. Ahern, “The mean modulus and the derivatives of inner functions,” Indiana Univ. Math. J.,28, No. 2, 311–348 (1979).Google Scholar
  17. 17.
    Yu. G. Reshetnyak, “On the concept of capacity in the theory of functions with generalized derivatives,” Sib. Mat. Zh.,10, No. 5, 1109–1138 (1969).Google Scholar
  18. 18.
    V. G. Maz'ya and V. P. Khavin, “Nonlinear potential theory,” Usp. Mat. Nauk,27, No. 6, 67–138 (1972).Google Scholar
  19. 19.
    I. É. Verbitskii, “Inner functions as multipliers on the spaces Dα,” Funkts. Anal. Prilozhen.,16, No. 3, 48–49 (1982).Google Scholar
  20. 20.
    I. É. Verbitskii, “On multipliers in the spaces ZAP,” Funkts. Anal. Prilozhen.,14, No. 3, 67–68 (1980).Google Scholar
  21. 21.
    I. P. Natanson, Theory of Functions of a Real Variable [in Russian], Nauka, Moscow (1974).Google Scholar
  22. 22.
    N. K. Nikol'skii, Lectures on the Shift Operator [in Russian], Nauka, Moscow (1980).Google Scholar
  23. 23.
    E. M. Stein, Singular Integrals and Differential Properties of Functions [Russian translation], Mir, Moscow (1973).Google Scholar
  24. 24.
    T. M. Flett, “Lipschitz spaces of functions on the circle and the disc,” J. Math. Anal. Appl.,39, No. 1, 125–158 (1972).Google Scholar
  25. 25.
    J. Peetre, New Thoughts on Besov Spaces, Duke Univ. Math. Series, No. 1, Duke Univ., Durham, NC (1976).Google Scholar
  26. 26.
    I. É. Verbitskii, “On Taylor coefficients and Lp-modulus of continuity of Blaschke products,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst Steklov (LOMI),107, 27–35 (1982).Google Scholar
  27. 27.
    V. G. Maz'ya, “On an embedding theorem and multipliers in pairs of Sobolev spaces,” Trudy Tbiliss. Mat. Inst.,66, 59–70 (1980).Google Scholar
  28. 28.
    I. I. Hirschman Jr., “A convexity theorem for certain groups of transformations,” J. Analyse Math.,2, No. 2, 209–218 (1953).Google Scholar
  29. 29.
    L. I. Hedberg, “On certain convolution inequalities,” Proc. Am. Math. Soc.,36, No. 3, 505–510 (1972).Google Scholar
  30. 30.
    T. Sjodin, “Capacities of compact sets in linear subspaces ofR n,” Pac. J. Math.,78, No. 2, 261–266 (1978).Google Scholar
  31. 31.
    D. R. Adams and N. G. Meyers, “Thinness and Wiener criteria for nonlinear potentials,” Indiana Univ. Math. J.,22, No. 2, 169–197 (1972).Google Scholar

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© Plenum Publishing Corporation 1985

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  • I. É. Verbitskii

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